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Wednesday, April 20, 2011

Fantasy Curriculum: All out assault on Math!

A few weeks ago (7 eons in internet time...) I posted on Engineer Blogs a snippet of ideas for how I would change the mechanical engineering curriculum. This mainly focused around one thing: have all ME required courses taught by ME faculty. It's pretty simple. If you're a ME student, you probably have ~120 hours of ME degree courses that you need to take. If they're all not taught by ME faculty, you're getting shafted in your education. That's just my opinion. However, it seemed from the initial comments that there's bunch of people that would like that.

In my original post, I picked on a few non-ME courses that I would like to see changed. Today, I'm going to specifically discuss the Mathematics and Statistics curriculum parts of a typical ME program and how I'd like to change them. I realize I'm totally biased and haven't had a good math teacher in college but I'm also going to assume I'm not alone in this boat.

The biggest reason for swapping math profs for ME profs is the application of the math. When you're in a math class (even math for engineers) it's always math for the sake of math. I took a graduate math course called "Advanced Applied Engineering Mathematics". There was never any actual applying of the math. Engineers don't care about math just because it's math. They want to use it. If you don't have examples of it, you're talking to zombies. Math prof's don't give practical examples. However, ME profs can.

This brings me to the second biggest reason for changing profs. Math profs want to teach math students who think like them and approach problems like them. ME profs want to teach to ME students who think like them and approach problems like them. It's pretty simple and basic but it doesn't make sense. And ME profs are as qualified (if not more qualified) to teach engineering math courses because they use it on a regular basis.

Most universities have the math courses front-loaded before the ME courses. A better approach is to actually teach the math in the same course where it's applied. I'll give you an example. One of the basic things about derivatives (and 2nd derivatives) and integrals is the relationship between position, velocity, and acceleration. I don't ever remember hearing those three words in my basic calc classes. That's a shame. Probably these concept should be taught as part of the basic physics course.

Now, rather than rant forever, I'll try to discuss some constructive things. I'm going to assume a student needs the following math courses (some universities may vary)

Calc I

Calc II

Calc III

Diff Eq

Linear Algebra

Statistics

For Calc I and II, I'd combine those into one course called Engineering Calc. I would keep derivatives, integrals (only shorthand methods), partial derivatives, equations of motion, and complex numbers/conjugates. Everything else, deep six it. You're not going to remember it anyway and if you need it later, you can learn it later. Also, I would hack down Calc III and Linear Algebra and combine them into one class called Multivariable Calc. You can only take some much of vectors intercepting a plane is space for so long before you kill yourself. And when you're talking about multi-variable problems, it probably good to introduce some matrices.

Statistics, I would kill completely. Totally useless course except for the first 2 concepts you learn about standard deviations and distributions. Everything else in the course was of the theory of statistics persuasion which is useless for UG engineers. Instead, I would tack that on to a lab course. I'll go back over this when I talk about chemistry.

Lastly, Diff Eq. Wow, words cannot begin to express how much I disliked Diff Eq. However, it is needed for Fluids, Vibrations, and Heat Transfer so it has to stay. It depends on how the curriculum is set up, but I think most students take this during their Sophomore year. Instead, I would pick whichever class needs it and shows up first (say Fluids) and have it co-taught with that class. This way, you'd take 6 hours of Diff Eq and Fluids but the profs would have to work in tandem. I know it's tough but we're trying to get the students to learn more useful information.

I think the math curriculum can be trimmed from 18 hours to 9 hours with some supplemental stuff added to a few courses. That frees a lot of space for other courses. I'm slowly building to my complete Fantasy Curriculum. Over the next few days, I'll tackle some more subjects. Thoughts on my assault on math?

7 comments:

I have never felt as though I should have been taught *less* math. My statistics class did focus on deviation and distributions almost entirely, with a brief section on probability, which is very handy in statistical mechanics (i.e., materials Thermodynamics). I must admit, that being a computationalist, I find math more useful on a daily basis than I would in other situations.

If anything, I felt there were two very large gaps in my math education: wave vector math (div, grad and curl) and tensor math. The first is critical for anything in electromagnetics, and the later is critical for elastic properties and mechanics.

In regards to calculus, I honestly did hear position, velocity, acceleration ( and jerk and snap) in reference to the order of derivatives. There are math professors in the world that give practical examples (particularly if they have an obsession with roller coasters...).

My issue with concurrent teaching is that for many students, they learn a subject more effectively when they see it more than once. By this, I mean that they may be taught vector calculus in math, but truly grasp it in Mechanics of Materials, not because the second time it is taught with better examples or clearer explanations, but simply because it is the second time they've seen the material.

I do feel the general math curriculum could be streamlined, but mostly by skipping or compressing specific topics. Numeric integration, for example, shouldn't take more than two class periods at absolute maximum. Vector addition, subtraction and multiplication also do not require multiple weeks: allegedly, students learned that before they got to college.

I have to be honest that I still think this is a bad idea. I had a physics prof who once explained a bunch of math concepts stating that they were true by "the principle of no good reason." I ended up spending more time in the math department than in physics that semester, getting help from a math prof because he actually understood what was going on mathematically.

Ok, but I did leave some vital portions of my explanation out. If you streamlined the "early math", which I would say is more math for the sake of math than actual useful stuff, you could then add more later.

For instance, if you reduced Calc 1 and 2 into one class, and Calc 3 and Lin Alg into another, you could free up 1 extra ME elective and 1 extra Higher level (senior level) math. In this case, the student probably would get more math out of it.

They would get the basic math needed for their core ME classes. Plus, once they're seniors, they are probably more dedicated, and probably know how to learn more on their own. If you give them a more advanced math then (but still make it useful), you wouldn't completely get rid of all math, just the BS early portions that they're not going to remember anyway.

We actually had differential equations split into two courses (ordinary and partial).

I think dropping the proofs from Calc I and II would probably allow you to compress them into one course fairly easily. I had also completely forgotten Linear Algebra (taken in 1A) by the time we used it for anything in Engineering classes - maybe moving it a bit later would help?

Just stumbled across this (and the Engineering Blog, which is how I found you - it's a slow day at work).

I disagree almost 100%. I was a UG in physics, with an MEng. Statistics is probably the most vital math course in my professional career, with calculus (including Diff Eq) and Lin Alg hot on its heels. It's amazing that some of my fellow MEng students, who learned statistics through a 'math for engineers' course in their major, didn't understand the basics of probability which led to stats. They knew they 'had to' do an F-test, for example, but not why or what its results mean. Don't get me started on abuses of p-values.

I don't disagree that some of these courses could be streamlined (numeric integration is a glaring example, with us now being in the 21st century and using current computing technology). As for deep-sixing a lot of this stuff, or locating it to a 'home' department? I don't think it's a great idea. Engineering profs, whose focus is on application, don't always communicate the motivation behind the physics and math material those courses. The deeper knowledge is important to critical thinking skills and the whole 'learning how to learn' process that really seems to be the point of any UG curriculum.

Finally, in my opinion, analogic thought processes are almost more important than technical skills in day-to-day engineering. You don't necessarily get exposure to different subjects within your 'home' field. It's a trope, sure, but if you have a problem, it's likely that someone, somewhere, has solved something similar.

About GEARS

GEARS is a tenure track assistant professor of Mechanical Engineering and Optics at a small, private R1 university. GEARS blogs about his experience going through the tenure track process and all the trappings of Grads, Engineering, Academia, Research, and Students. His random musings are solely his own and do not necessarily reflect the views of SnowU. He can be reached at prof dot gears at gmail dot com.